 
 (expect 0.5165
         (round-double (lower-surface-x-function (NACA-design 9.5 9 40) 0.5)))
+
+;;----------gradient-forward-polar-function ------------
+(expect 0.0000
+        (round-double (gradient-forward-polar-function (NACA-design 0 0.5 20) 0.5)))
+
+(expect -0.0234
+        (round-double (gradient-forward-polar-function (NACA-design 4.75 4.5 100) 1.5708)))
+
+(expect 0.0938
+        (round-double (gradient-forward-polar-function (NACA-design 9.5 9 40) 4.71239)))
+
+;;----------gradient-aft-polar-function ------------
+(expect 0.000
+        (round-double (gradient-aft-polar-function (NACA-design 0 0.5 20) 0.5)))
+
+(expect -0.0156
+        (round-double (gradient-aft-polar-function (NACA-design 4.75 4.5 100) 1.5708)))
+
+(expect 7.6
+        (round-double (gradient-aft-polar-function (NACA-design 9.5 9 40) 4.71239)))
+
+;;-------- theta-switch ----------
+(expect 1.5708
+        (round-double (theta-switch (NACA-design 5 5 5))))
 
 ;;;-------- riemann-sum ----------
 (expect 0.0681

        (round-double (area (NACA-design 3 40 12)))) ;; assymetric -- thin foil
(expect 0.1367
        (round-double (area (NACA-design 9.5 0 20)))) ;; assymetric -- thick foil

  (:require [expectations :refer :all]
            [hydrofoil.model :refer :all]
            [hydrofoil.core :refer :all]
            [hydrofoil.evolution :refer :all]
            [hydrofoil.utils :refer :all]))

;;; --------- thickness-function tests ------------
; thickness 0:
